Determine the intercepts of the line. $-3x-4=-5y-8$ $y$ -intercept: $\Big($
Solution: The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $ \begin{aligned}-3\cdot0-4&=-5y-8\\ -4&=-5y-8\\ 5y&=-4\\ y&=-\dfrac{4}{5}\end{aligned}$ So the $y$ -intercept is $\left(0,-\dfrac{4}{5}\right)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $ \begin{aligned}-3x-4&=-5\cdot{0}-8\\ -3x-4&=-8\\ -3x&=-4\\ x&=\dfrac{4}{3}\end{aligned}$ So the $x$ -intercept is $\left(\dfrac{4}{3},0\right)$. In conclusion, The $y$ -intercept of the graph is $\left(0,-\dfrac{4}{5}\right)$. The $x$ -intercept of the graph is $\left(\dfrac{4}{3},0\right)$.